You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
115 lines
3.1 KiB
115 lines
3.1 KiB
% Sets
|
|
\newcommand{\N}{\mathbb{N}}
|
|
\newcommand{\Z}{\mathbb{Z}}
|
|
\newcommand{\R}{\mathbb{R}}
|
|
\newcommand{\D}{\mathcal{D}}
|
|
\newcommand{\T}{\mathcal{T}}
|
|
\newcommand{\Ell}{\mathcal{L}}
|
|
|
|
% Random Variable
|
|
\newcommand{\rv}[1]{\bm{#1}}
|
|
\newcommand{\map}[1]{#1^{\text{MAP}}}
|
|
% Matrix
|
|
\newcommand{\mat}[1]{\bm{#1}}
|
|
\newcommand{\inv}{^{\raisebox{.2ex}{$\scriptscriptstyle-\mkern-1.5mu1$}}}
|
|
\newcommand{\tran}{^{\mkern-1.5mu\raisebox{.2ex}{$\scriptscriptstyle\mathsf{T}$}}}
|
|
\newcommand{\itran}{^{\raisebox{.2ex}{$\scriptscriptstyle-\mkern-1.5mu\mathsf{T}$}}}
|
|
\newcommand{\Eye}{\mat{\mathrm{I}}}
|
|
% Pseudo Inputs
|
|
\newcommand{\ps}[1]{\bar{#1}}
|
|
\newcommand{\psmat}[1]{\ps{\mat{#1}}}
|
|
|
|
% Nicer empty set
|
|
\renewcommand{\emptyset}{\varnothing}
|
|
|
|
% Math operators
|
|
% General
|
|
\DeclareMathOperator{\id}{id}
|
|
\DeclareMathOperator*{\argmax}{argmax}
|
|
\DeclareMathOperator*{\argmin}{argmin}
|
|
\DeclareMathOperator{\atanTwo}{atan2}
|
|
\DeclareMathOperator{\sgn}{sgn}
|
|
\DeclareMathOperator{\diag}{diag}
|
|
\DeclareMathOperator{\tr}{tr}
|
|
\DeclareMathOperator*{\maximize}{maximize}
|
|
\DeclareMathOperator*{\minimize}{minimize}
|
|
\DeclareMathOperator{\subjectto}{subject\ to}
|
|
\DeclareMathOperator{\Oh}{\mathcal{O}}
|
|
\DeclareMathOperator{\softmax}{softmax}
|
|
\newcommand{\Powerset}[1]{2^{#1}}
|
|
\newcommand*{\diff}{\mathop{}\!\mathrm{d}}
|
|
\DeclarePairedDelimiter{\abs}{\vert}{\vert}
|
|
\newcommand{\nth}[2][th]{#2^{\text{#1}}}
|
|
|
|
% Probabilities
|
|
\DeclareMathOperator{\E}{\mathbb{E}}
|
|
\DeclareMathOperator{\cov}{cov}
|
|
\DeclareMathOperator{\var}{var}
|
|
\DeclareMathOperator{\corr}{\varrho}
|
|
\DeclareMathOperator{\p}{p}
|
|
\DeclareMathOperator{\q}{q}
|
|
\DeclareMathOperator{\KLdiv}{KL}
|
|
\DeclareMathOperator{\K}{\mathcal{K}}
|
|
\DeclareMathOperator{\Q}{\mathcal{Q}}
|
|
\DeclareMathOperator{\Norm}{\mathcal{N}}
|
|
\DeclareMathOperator{\Multi}{\mathcal{M}}
|
|
\DeclareMathOperator{\Ber}{\mathcal{B}}
|
|
\DeclareMathOperator{\Uni}{\mathbb{U}}
|
|
\DeclareMathOperator{\Ind}{\mathbb{I}}
|
|
\DeclareMathOperator{\GP}{\mathcal{GP}}
|
|
\DeclareMathOperator{\SPGP}{\mathcal{SPGP}}
|
|
\DeclareMathOperator{\indep}{\perp\mkern-9.5mu\perp}
|
|
\DeclareMathOperator{\nindep}{\centernot{\indep}}
|
|
|
|
\providecommand\given{}
|
|
\DeclarePairedDelimiterX{\Cond}[1]{(}{)}{
|
|
\renewcommand\given{%
|
|
\nonscript\mkern2mu
|
|
\delimsize\vert
|
|
\nonscript\mkern2mu
|
|
\mathopen{}
|
|
\allowbreak}
|
|
#1
|
|
}
|
|
|
|
\makeatletter
|
|
\newcommand{\Fun}{\@ifstar\@sfun\@fun}
|
|
\newcommand{\@fun}[1]{#1\Cond}
|
|
\newcommand{\@sfun}[1]{#1\Cond*}
|
|
\makeatother
|
|
|
|
\newcommand{\Prob}{\p\Cond}
|
|
\newcommand{\aProb}{\tilde{\p}\Cond}
|
|
\newcommand{\Variat}{\q\Cond}
|
|
\newcommand{\Gaussian}{\Norm\Cond}
|
|
\newcommand{\Multinomial}{\Multi\Cond}
|
|
\newcommand{\Uniform}{\Uni\Cond}
|
|
\newcommand{\Indicator}{\Ind\Cond}
|
|
|
|
\DeclarePairedDelimiterX{\KLdelim}[2]{(}{)}{%
|
|
#1\mkern2mu\delimsize\|\mkern2mu#2%
|
|
}
|
|
\newcommand{\KL}{\KLdiv\KLdelim}
|
|
|
|
\DeclarePairedDelimiterXPP{\Moment}[2]{#1}{[}{]}{}{
|
|
\renewcommand\given{%
|
|
\nonscript\mkern2mu
|
|
\delimsize\vert
|
|
\nonscript\mkern2mu
|
|
\mathopen{}
|
|
\allowbreak}
|
|
#2
|
|
}
|
|
|
|
\providecommand\with{}
|
|
\DeclarePairedDelimiterX{\Set}[1]{\{}{\}}{
|
|
\renewcommand\with{%
|
|
\nonscript\mkern2mu
|
|
\delimsize\vert
|
|
\nonscript\mkern2mu
|
|
\mathopen{}
|
|
\allowbreak}
|
|
#1
|
|
}
|
|
|
|
\DeclarePairedDelimiterXPP{\pix}[1]{\begingroup\scriptscriptstyle}{(}{)}{\endgroup}{\mkern-2mu#1\mkern-2mu}
|